Temperature and purity dependence of the nuclear-spin relaxation rate in the gapless region of type-II superconductors

Abstract

The volume average of the nuclear-spin relaxation rate in type-II superconductors,R _s, is calculated for magnetic fields slightly below the upper critical field and all mean free paths,l, and temperatures. It is found to be expressible solely in terms of the volume average of the density of states,$\bar N(\omega )$, where the latter quantity has been determined recently byNeumann for alll. The derivation is based onHelfand andWerthamer's eigen-value equation for the order parameter,Δ. The deviation of$\bar R_s$ from the relaxation rate in the normal state,R _n, is proportional to the quantity$[|\overline {\Delta |^2 } /\Delta _{BCS}^2 (T)]R_n$ (the bar denotes the spatial average). The proportionality factor is found to decrease monotonously as the temperature decreases and/orl increases. This behavior is closely related to the fact that$\bar N(\omega )$ shows no gap for the excitation energiesω and decreases asl increases, in particular at energiesω close to zero (ω=0 corresponds to the Fermi energy).